Answer:

Solution. substitute x = 2 in L.H.S. Substitute x = 3 in L.H.S. k = and m = 9.

Verified answer

Since x=2 and x=3 are roots of the equation 3x 2 −2kx+2m=0⇒12−4k+2m=0⇒2k−m=6 ...(i)and ⇒27−6k+2m=0⇒6k−2m=27 ...(ii)On multiplying (i) by 3 and subtracting (ii) from it, we get6k−3m=18−6k +

− 2m= -27 −m=−9

−m=−9∴m=9

−m=−9∴m=9On putting m=9 in (i), we get

−m=−9∴m=9On putting m=9 in (i), we get2k=15⇒k= 215

−m=−9∴m=9On putting m=9 in (i), we get2k=15⇒k= 215∴(k,m)=(215 ,9)